A Frequency-Domain Approach to Nonlinear Negative Imaginary Systems Analysis

Di Zhao; Chao Chen; Sei Zhen Khong

A Frequency-Domain Approach to Nonlinear Negative Imaginary Systems Analysis

Systems and Control 2021-10-01 v1 Systems and Control

Authors: Di Zhao , Chao Chen , Sei Zhen Khong

Abstract

In this study, we extend the theory of negative imaginary (NI) systems to a nonlinear framework using a frequency-domain approach. The extended notion is completely characterized via a finite-frequency integration over a "kernel function" on energy-bounded input and output signal pairs. The notion is closely related to and carefully contrasted with the well-studied extension of negative imaginariness -- the theory of counterclockwise dynamics. A condition for feedback stability of the proposed nonlinear NI systems is then developed based on the technique of integral quadratic constraints. Examples and simulations on feedback interconnections of typical nonlinear systems are provided to demonstrate the effectiveness.

Keywords

nonlinear dynamics and control modal decomposition analysis stability analysis and control

Cite

@article{arxiv.2109.15126,
  title  = {A Frequency-Domain Approach to Nonlinear Negative Imaginary Systems Analysis},
  author = {Di Zhao and Chao Chen and Sei Zhen Khong},
  journal= {arXiv preprint arXiv:2109.15126},
  year   = {2021}
}

Comments

This paper has been submitted to Automatica

A Frequency-Domain Approach to Nonlinear Negative Imaginary Systems Analysis

Abstract

Keywords

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